On the Real Zeros of Positive Semidefinite Biquadratic Forms

DOI10.1080/00927872.2013.865052zbMath1318.14055OpenAlexW1998292266MaRDI QIDQ5249922

Ronan Quarez

Publication date: 13 May 2015

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927872.2013.865052

zbMATH Keywords

sums of squarespositive semidefinitereal zerosbiquadratic forms

Mathematics Subject Classification ID

Quadratic and bilinear forms, inner products (15A63) Real algebraic and real-analytic geometry (14P99) Forms over real fields (11E10)

Related Items (6)

On the extreme rays of the cone of \(3\times 3\) quasiconvex quadratic forms: extremal determinants versus extremal and polyconvex forms ⋮ New examples of extremal positive linear maps ⋮ The multidimensional truncated moment problem: the moment cone ⋮ A note on the extreme points of the cone of quasiconvex quadratic forms with orthotropic symmetry ⋮ Polynomial diffusions on compact quadric sets ⋮ Real zeros of SONC polynomials

Cites Work

• Real zeros for positive semidefinite forms. I
• Estimates of the Pythagoras number of \(\mathbb R_m[x_1, \ldots , x_n\) through lattice points and polytopes]
• Completely positive linear maps on complex matrices
• Positive semidefinite biquadratic forms
• Hermitian matrices over polynomial rings
• Self-adjoint determinantal representations of real plane curves
• Die Darstellung biquadratischer Formen als Summen von Quadraten mit Anwendung auf die Variationsrechnung
• Linear matrix inequality representation of sets
• Cayley-Bacharach theorems and conjectures

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